Partial interconnection and observer-based dead-beat control of two-dimensional behaviors

Abstract

In this paper the dead-beat control problem, by partial interconnection, of two-dimensional (2D) discrete behaviors, defined on the grid $$\mathbb{Z }_+\times \mathbb{Z }$$ Z + × Z and having the time as (first) independent variable, is investigated. The possibility of driving to zero (in a finite number of "steps") either all or part of the system variables, by means of a partial interconnection controller, proves to be equivalent to the reconstructibility of the variables that are not accessible for control. On the other hand, if we search for "admissible" dead-beat controllers, the only ones providing meaningful results in practice, we have to introduce the zero-time-controllability assumption. These two properties are just the necessary and sufficient conditions for the existence of an observer-based (admissible) dead-beat controller, which consists of a dead-beat observer, to estimate the relevant variables from the measured ones, and of a full interconnection dead-beat controller, acting on both the measured and the estimated variables.